This report contains different plots and tables that may be relevant for analysing the results. Observe:
alg1Given a problem consisting of \(m\)
subproblems with \(Y_N^s\) given for
each subproblem \(s\), we use a
filtering algorithm to find \(Y_N\)
(alg1).
Note that the width of objective \(i\), \(w_i = [l_i, u_i]\) should be approx. \(10000m\):
## # A tibble: 3 × 6
## m mean_width1 mean_width2 mean_width3 mean_width4 mean_width5
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2 19347. 19300. 19337. 19184. 18974.
## 2 3 27966. 28031. 27494. 27717. 26398.
## 3 4 38029. 38259. 37875. NaN NaN
What is \(|Y_N|\) given the different methods of generating the set of nondominated points for the subproblems?
## # A tibble: 4 × 3
## method mean_card n
## <chr> <dbl> <int>
## 1 l 40915. 110
## 2 m 45295. 110
## 3 u 39512. 110
## 4 ul 38208. 110
Does \(p\) have an effect?
## # A tibble: 16 × 4
## # Groups: method [4]
## method p mean_card n
## <chr> <dbl> <dbl> <int>
## 1 l 2 2781. 30
## 2 m 2 2260. 30
## 3 u 2 708. 30
## 4 ul 2 717. 30
## 5 l 3 10765. 30
## 6 m 3 9864. 30
## 7 u 3 3093. 30
## 8 ul 3 3998. 30
## 9 l 4 63447. 25
## 10 m 4 84820. 25
## 11 u 4 66024. 25
## 12 ul 4 62641. 25
## 13 l 5 100325. 25
## 14 m 5 99928. 25
## 15 u 5 103271. 25
## 16 ul 5 99817. 25
Does \(m\) have an effect?
## # A tibble: 12 × 4
## # Groups: method [4]
## method m mean_card n
## <chr> <dbl> <dbl> <int>
## 1 l 2 45336. 80
## 2 m 2 53458. 80
## 3 u 2 44689. 80
## 4 ul 2 43026. 80
## 5 l 3 38087. 20
## 6 m 3 31557. 20
## 7 u 3 37214. 20
## 8 ul 3 35707. 20
## 9 l 4 11207. 10
## 10 m 4 7464. 10
## 11 u 4 2700. 10
## 12 ul 4 4666. 10
We classify the nondominated points into, extreme, supported non-extreme and unsupported.